摘要
令A>0及B>0记两个n×n(n≥2)厄尔米特正定矩阵;μ_1≥μ_2≥…μ_n及ν_1≥ν_2≥…≥ν_n记A和B的特征值;设λ为AB的任意特征值.ShaHu-yun证得2/nμ_n^2ν_n^2/μ_n^2+ν_n^2<λ<n/2(μ_2~1+μ_1~2)
Let A and B be two n×n (n≥2) positive definite hermitian matrices (A>0 and B>0); μ_1≥μ_2≥……≥μ_n and ν_1≥ν_2≥……ν_n are the eigenvalues of A, B; λ is any eigenvalue of AB. In this paper, we have got a new bound on λ which is much better than [1] in other simple method. Mainresult is 1/2μ_nν_n<λ<nμ_1ν_1.
出处
《应用数学与计算数学学报》
1990年第2期89-90,共2页
Communication on Applied Mathematics and Computation
